SSL II USER'S GUIDE - Lahey Computer Systems

14
Symbol Example Meaning Remarks
∑
n
∑ x i
i=
m
Summation (xm ,..., xn) Sum cannot be given if n < m
n
If ∑ x i summation excludes xl.
∑ i+
j
i
x 2 Summation with respect to i
y′, f ′(x)
dy df ( x)
y′
= , f ′ ( x)
=
dx dx
For n-order derivative:
f (n) n
d f ( x)
(x) = n
dx
z Absolute value of z If z = a + ib
max max(x1 , ..., xn) The maximum value of (x1, ..., xn)
min
max xi
i
min(x1 , ..., xn)
The minimum value of (x1, ..., xn)
sign
min xi
i
sign(x)
Sign of x
log log x Natural logarithm of x
Re Re(z) Real part of complex number z
Im Im(z) Imaginary part of complex number z
arg Arg z Argument of complex number z
δ ij
Kronecker’s delta
γ Euler’s constant
π Ratio of the circumference of the circle to its diameter
i z = a + ib Imaginary unit
P.V.
P.V.
x
∫− ∞
e
t
t
dt
a1
a2
b0
+ + + ⋅⋅
⋅
b b
1
2
Principal value of an integral
Continued fraction
∈ x ∈ X Element x is contained in set X.
x x = ϕ(x
)
All elements of set x satisfy the equation.
{ | } { }
C k k
f ( x)
∈ C [ a,
b]
f (x) and up to k-th derivatives are continuous in the
interval [a , b].
i=
m
i≠l
2
z = a + b
When x is positive, 1.
When x is negative, -1.
Note: This table defines how each symbol is used in this guide. A symbol may have a different meaning elsewhere. Commonly used
symbols, such as + and – , were not included in the list.
i =
−1
2